Algebraic Identities

Q.

Question 86 (xiv)

Using suitable identities, evaluate the following:

$9.8\times 10.2$

Q. Write the given set in Roster Form:

(b) The squares of the first four natural numbers.

Q.

Question 86 (xi)

Using suitable identities, evaluate the following:

$101\times 103$

Q. Write in the form of an algebraic expression:
iv) Surface area of a cube is six times the square of its edge

Q.

What are the possible ways in which 16 can be arranged as rectangles and squares?

Q. $(a-b{)}^2$ = _____.

1. $a^2-2ab+b^2$
2. $a^2+2ab+b^2$
3. $a^2-2ab-b^2$
4. $a^2+2ab-b^2$

Q.

Evaluate $136\times 107$.

1. $14552$

2. $14551$

3. $14562$

4. $13552$

Q.

Expand the following identities : ${(2a+3b)}^2$

Q. Using suitable identity, evaluate $136\times 107$

1. 14552

Q. Find the sum of the first five odd numbers and check whether the sum is a square number or not.

Q. $(a+b{)}^2$ = _____.

1. $a^2+2ab+b^2$
2. $a^2+2ab-b^2$
3. $a^2-2ab-b^2$
4. $a^2-2ab+b^2$

Q.

$(x+y)(x-y)(x^2+y^2)$ = ___________.

1. $x^3-y^3$

2. $x^3+y^3$

3. $x^4+y^4$

4. $x^4-y^4$

Q. A square pyramid was placed on top of a rectangular prism to make a dollhouse. The dimensions of the dollhouse are given below. Robin wants to decorate her dollhouse with stickers of $1$ square inch each. Calculate the number of stickers required to cover all outer faces of the dollhouse.

1. $1084\text{sq in}$
2. $1728\text{sq in}$
3. $2484\text{sq in}$
4. $2084\text{sq in}$

Q. Jenny and her friends picked out some paper chits from a glass bowl. Each of these chits had some numbers on them.
Jenny's chit had the number 16.
Kaira's chit had a number that was the square root of the number on Jenny's chit.
Also, Sia's chit had a number that was the square root of the number on Kaira's chit.

Which of the following numbers appeared on Sia's chit?

1. 2
2. 8
3. 32
4. 4

Q.

In a calender, sum of any four number taken in a block can always be written as

1. 4(x + 2)

2. 2(x + 2)

3. 4(x + 4)

4. 2(x + 4)

Q. One side of the base of a square base prism A is increased by \(50\)% and the other side is decreased by \(50\)% keeping the height of the prism \(10\) cm in both cases. If the side of the square is a, then what change in the total surface area of the prism is expected?

Q. Write the given set in Roster Form:

(d) Single digital number that are ​perfect squares as well.

Q. Divide the following and write your answer in lowest terms: $\frac{3x^2-x-4}{9x^2-16}÷\frac{4x^2-4}{3x^2-2x-1}$

1. $\frac{3x+1}{4(3x+4)}$
2. $\frac{3x-1}{4(3x+4)}$
3. $\frac{3x+1}{4(3x-4)}$
4. None of these

Q. Question 90 (vi)

Factorise the following, using the identity, $a^2-2ab+b^2=(a-b{)}^2$.

$p^2.y^2-2py+1$

Q. If $a=-3$ and $x=2$, find the value of the expression $\frac{3ax+7a-11}{5ax-3a+1}$.

1. $\frac{5}{2}$
2. $\frac{1}{2}$
3. $7$
4. $-3$

Q. While playing with blocks, Tim wants to form a cube using rectangular prisms with the given dimensions. Which of the following is the correct number of blocks that will be required?

1. 36
2. 18
3. 6
4. 12

Q. Fill in the blank: ______ – 15 = – 10

1. +15
2. -25
3. -15
4. +5

Q. If $m=3$ and $n=7$, evaluate :

iv) $4n^2$

Q. A castle wall made up of stone has four windows with its dimensions, as shown below:

Find the area covered with stones on the wall.
HINT: The area covered by stones equals the area of the wall minus the area of the windows.

1. $\frac{191}{14}\text{sq ft}$
2. $\frac{191}{41}\text{sq ft}$
3. $\frac{20}{7}\text{sq ft}$
4. $\frac{191}{20}\text{sq ft}$

Q. If $a=-10$, evaluate :

ii) $a^2+8a$

Q.

Find:(–7) + (–8) + (–90)

Q.

Determine whether the given statement is true or false.

The triangular numbers follow this pattern:​

The first two numbers are odd, followed by two even numbers, then two odd numbers, and so on.​

Q.

Using special products, simplify :

$(x-15)(x+11)$

Q. Write in the form of an algebraic expression:​
(iv)Surface area of a cube is six times the square of its edge​.

Q. Divide
$(y^3-3y^2+5y-1)÷(y-1)$